$\dfrac{ 5s + 2t }{ 8 } = \dfrac{ 9s - 9u }{ -8 }$ Solve for $s$.
Notice that the left- and right- denominators are opposite $\dfrac{ 5s + 2t }{ {8} } = \dfrac{ 9s - 9u }{ -{8} }$ So we can multiply both sides by $8$ ${8} \cdot \dfrac{ 5s + 2t }{ {8} } = {8} \cdot \dfrac{ 9s - 9u }{ -{8} }$ $5s + 2t = - \cdot \left( 9s - 9u \right) $ Distribute the negative sign on the right side. $5s + 2t = -9s + 9u$ ${5}s + {2}t = -{9}s + {9}u$ Combine $s$ terms on the left. ${5s} + 2t = -{9s} + 9u$ ${14s} + 2t = 9u$ Move the $t$ term to the right. $14s + {2t} = 9u$ $14s = 9u - {2t}$ Isolate $s$ by dividing both sides by its coefficient. ${14}s = 9u - 2t$ $s = \dfrac{ 9u - 2t }{ {14} }$